Correction to terminology (Pat Donaly)

Correction to terminology (Pat Donaly)

[Jpdonaly]

Jean Pradines has kindly corrected my usage of "intertwining function". I
erred in attempting to extend this term to the variant naturality concept
described but not named by Mac Lane in problem 5, page 19 of either edition of
"Categories for the Working Mathematician". To within order of the functors which
are involved, this problem describes a natural transformation from functor F:A-->
B to parallel functor G:A-->B to be a function t which satisfies the left and
right transformation laws

t(ab)=G(a)t(b)=t(a)F(b)

when ab is defined in A. (The pair (G,F) is implicitly part of the natural
transformation.)  If A is a group with object u and G and F are group actions,
then the value t(u) is a classical intertwining function, whereas I have been
calling t an intertwining function. I apologize to all of those who had any of
their time wasted in wondering about this connection.

I still need terminology for t much more than I need the intertwining
function idea; so, from now on, I intend to use "entwining function" to refer to t,
but, if this conflicts with more standard usage or if there is already a
standard word for t, I would appreciate being told.

Pat Donaly